Problem: Solve for $x$ and $y$ using elimination. ${5x-y = 9}$ ${6x+y = 13}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $11x = 22$ $\dfrac{11x}{{11}} = \dfrac{22}{{11}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x-y = 9}\thinspace$ to find $y$ ${5}{(2)}{ - y = 9}$ $10-y = 9$ $10{-10} - y = 9{-10}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 2}$ into $\thinspace {6x+y = 13}\thinspace$ and get the same answer for $y$ : ${6}{(2)}{ + y = 13}$ ${y = 1}$